Problem: Rewrite as a simplified fraction. ${0.6\overline{5} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 65.5555...\\ 10x &= 6.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 59}$ ${x = \dfrac{59}{90}} $